Given an undirected graph \(\mathcal {G}=\lbrace \mathcal {V, E}\rbrace \)  with \(C\)  classes, where \(\mathcal {V} = \lbrace v_{1}, v_{2}, \dots , v_{N}\rbrace \) , \(\mathcal {E}\) , and \(N\)  are the node set, edge set, and the number of nodes, respectively. In classic graph learning, a graph is usually characterized by its attribute matrix \(\mathbf {X} \in \mathbb {R}^{N \times D}\)  and normalized adjacency matrix \(\widetilde{\mathbf {A}} \in \mathbb {R}^{N \times N}\) , where \(D\)  is the node attribute dimension [1]}.
Specially, in attribute-missing graph learning, with the existence of missing attributes, we further define \(\mathcal {V}^{o} = \lbrace v_{1}^{o}, v_{2}^{o}, \dots , v_{N_{o}}^{o}\rbrace \)  and \(\mathcal {V}^{m} = \lbrace v_{1}^{m}, v_{2}^{m}, \dots , v_{N_{m}}^{m}\rbrace \)  to be the set of attribute-observed nodes and the set of attribute-missing nodes, respectively.
Accordingly, \(\mathcal {V}\)  = \(\mathcal {V}^{o}\)  \(\cup \)  \(\mathcal {V}^{m}\) , \(\mathcal {V}^{o}\)  \(\cup \)  \(\mathcal {V}^{m}\)  = \(\varnothing \)  and \(N\)  = \(N_{o}\)  + \(N_{m}\) .
In this circumstance, the missing attributes in \(\mathbf {X}\)  is firstly filled with all zeros and the resulting matrix is denoted as \(\widetilde{\mathbf {X}} \in \mathbb {R}^{N \times D}\) .
To introduce high-order adjacent information, we construct a series of adjacent matrices of different orders \(\mathcal {A} = \lbrace \mathbf {A}^{\textit {1}}, \mathbf {A}^{\textit {2}}, \dots , \mathbf {A}^{H}\rbrace \) , where \(\mathbf {A}^{h} \in \mathbb {R}^{N \times N}\) , \(H\)  is the number of orders. Specially, \(\mathbf {A}^{h} = \mathbf {A}^{\textit {1}}\mathbf {A}^{(h-1)}\) , where we denote \(\mathbf {A}^{\textit {0}}\)  as identity matrix \(\mathbf {I} \in \mathbb {R}^{N \times N}\) , 1 \(\le h \le H\) .
During the training, we manually mask partial connections on multi-order adjacent matrices to boost the network learning, thus \(\mathcal {A}\)  is redefined as \(\mathcal {\dot{A}} = \lbrace \mathbf {\dot{A}}^{\textit {1}}, \mathbf {\dot{A}}^{\textit {2}}, \dots , \mathbf {\dot{A}}^{H}\rbrace \) , where \(\mathbf {\dot{A}}^{h} \in \mathbb {R}^{N \times N}\) . Table REF  summarizes the commonly used notations.
